Question: Let $f(x) = -9x^{2}+7x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Answer: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}+7x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = 7, c = 6$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot -9 \cdot 6}}{2 \cdot -9}$ $ x = \dfrac{-7 \pm \sqrt{265}}{-18}$ $ x = \dfrac{-7 \pm \sqrt{265}}{-18}$ $x =\dfrac{-7 \pm \sqrt{265}}{-18}$